you have the matrix you are sending to the shader right? can't you do it in C++ code and send the resulting matrix as an extra parameter to the shader?

I can't.The matrix itself was generate in shader.In fact, I 'm trying to do normal mapping without precomputed tangent attribute in vertex buffer.The technique can be found in ShaderX5, Chapter2.6.It provides a non-orthogonal tangent-to-local matrix,so I'm trying to get the local-to-tangent matrix so that I can do lighting calculations in tangent space.

you have the matrix you are sending to the shader right? can't you do it in C++ code and send the resulting matrix as an extra parameter to the shader?

I can't.The matrix itself was generate in shader.In fact, I 'm trying to do normal mapping without precomputed tangent attribute in vertex buffer.The technique can be found in ShaderX5, Chapter2.6.It provides a non-orthogonal tangent-to-local matrix,so I'm trying to get the local-to-tangent matrix so that I can do lighting calculations in world space.